Open Access
Add to BibSonomyAbstract
The performance of a Talbot-Lau interferometer depends to a great extent on its visibility. This means, to obtain high quality phase-contrast and dark-field images a high visibility is mandatory. Several parameters influence the visibility of such a system, like for example the x-ray spectrum, the inter-grating distances or the parameters of the three gratings. In this multidimensional space, wave field simulations help to find the optimal combination of the grating specifications to construct a setup with a high visibility while retaining a fixed angular sensitivity. In this work we specifically analyzed the influence of the G1 grating duty cycle in simulations and experiments. We show that there is a lot of room for improvement by varying the duty cycle of the phase-shifting grating G1. As a result, by employing a third-integer duty cycle we can increase the visibility to up to 53 % in a laboratory setup with a polychromatic spectrum. The achieved visibility is more than two times higher compared to the result with a standard-type setup. This visibility gain allows a dose reduction by a factor of 5 preserving the same image quality.
© 2016 Optical Society of America
1. Introduction
In the last decade, several different techniques have been developed to overcome the weak soft-tissue contrast in conventional absorption-based x-ray imaging by measuring simultaneously the induced phase-shift [1]. Most of these approaches require highly brilliant x-ray sources like synchrotrons except for two methods called coded-aperture technique [2] and Talbot-Lau method [3–5], where the latter is used in this contribution. These two techniques work with conventional x-ray sources and can be adapted to existing medical imaging systems [6]. Several groups have shown promising results for medical imaging applications [7–11] as well as for non-destructive testing [12–16]. For quality assessment of a Talbot-Lau interferometer, the visibility is a crucial quantity. A high visibility delivers dark-field and phase-contrast images with a high image quality [17,18]. Several parameters influence the visibility of a Talbot-Lau system such as the x-ray spectrum or the specifications of the used gratings [19, 20]. In this work, we explore the influence of the parameters (period, height and duty cycle) of the phase-shifting grating G1 in simulation and experiment. We show that there is a lot of room for improvements if an appropriate combination of the G1 grating parameters is chosen.
2. Materials and methods
Measuring the real part δ of the refractive index n = 1 − δ + iβ is challenging because of the very small refraction angles of x-rays in the order of microradian [5]. By using an x-ray Talbot-Lau interferometer the differential phase signal can be measured. Additionally, the method offers a third signal which is named dark-field. This signal illustrates the loss of visibility due to small-angle scattering and refraction at object structures on length scales below the spatial resolution of the system [21].
The x-ray Talbot-Lau technique requires three gratings placed at certain distances between the x-ray tube and the x-ray detector, see Fig. 1. The phase-modulating grating G1 produces self-images of the grating in the intensity domain at certain distances downstream the grating due to the Talbot effect. As shown by Suleski [22] this happens at the named Talbot distances which are calculated by
where p1 denotes the period of the grating G1, n the Talbot order (odd-numbered for a π-shifting G1 and even for a π/2 grating) and λ the wavelength of the x-ray wave. For a π/2-shifting G1 η is equal to 1 and for a π-shifting grating η = 2. The period of the Talbot self-images depends on the way how the grating G1 shifts the phase of the x-ray wave. For a π-shifting grating the period is half the period of the modulating grating G1 and for a π/2-shifting grating it is exactly the same period. Therefore, it is possible to use a π-shifting grating G1 with a period of p1 and a π/2 grating with a period of p1/2 in the same Talbot distance
Fig. 1 Sketch of the Talbot-Lau interferometer: The phase grating G1 that produces Talbot self-images at certain distances behind the grating. These intensity patterns are scanned with the grating G2 due to the large pixel size of the used flat panel detector. To overcome the necessity of a small focal spot size, the source grating G0 is used in combination with a conventional medical x-ray tube exploiting the Lau-effect.
Because of the extended focal spot of conventional medical x-ray tubes a source grating G0 is mandatory to produce Talbot self-images. Otherwise the Talbot intensity pattern is smeared out. The period of the grating G0 is determined by the period of the Talbot self-image and the ratio between the distance from the grating G0 to the phase grating G1 and the Talbot distance dT. Due to the large pixel size in the order of 100µm of medical x-ray detectors and grating periods in the order of only a few micrometers, the intensity pattern cannot be resolved directly but has to be sampled with another grating, the analyzer grating G2. Therefore, the analyzer grating is shifted in fractions of the self-image’s periodicity perpendicular to the grating bars and images are taken at different position of G2. This method is referred to as phase stepping technique [5].
To determine the visibility of the experimental setup, a sinusoidal function
is fitted to the dataset obtained from the phase-stepping procedure. Thus the mean intensity I0, the amplitude A and the phase-shift φ can be extracted. The visibility V is calculated as the ratio between the amplitude A and the offset I0 of the phase-stepping curve:3. Simulation
To evaluate the influence of the G1 grating parameters on the performance of the x-ray interferometer a wave field simulation [23] is performed. There, the wave function Ψ(x) is calculated as a function of x where x represents an axis perpendicular to the propagation axis z and the axis of the grating bars y (see Fig. 1). The influence of the gratings G1 and G2 is calculated in the projection approximation [24]. The focal spot size of the medical x-ray tube and the influence of the G0 grating is considered by a convolution of the wave function with the grating aperture and the focal spot intensity distribution. For a detailed explanation of the wave-field simulation see [23].
The 24.39µm period absorption grating G0 presents a gold height of 150µm (±20µm); the 2.4µm period absorption grating G2 a gold thickness of 90µm (±10µm). Both gratings have a duty cycle of 0.5 (±0.01). The duty cycle is defined as dc = b/p where b denotes the width of the grating bars and p the period of the grating. The simulations are carried out in the second Talbot distance for a design energy of 25keV and a π/2-shifting G1 grating which results in a talbot distance dT = 0.0846m. This distance is fixed for all further investigations in order to keep the angular sensitivity constant. The influence of the G1 duty cycle (from 0.2 to 0.8) on the visibility as a function of the height and the period is investigated using simulations for the two periods 4.37µm and 2.185µm and for gold heights varying from 1µm to 15µm. Calculations were done for a standard 40kVp tungsten spectrum, as it is delivered from the manufacturer of our x-ray tube [25].
4. Experiments
Motivated by the results of the simulations, we fabricated different G1 gratings in order to test the simulation predictions with according measurements.
Our measurements are carried out with a Siemens MEGALIX x-ray tube and a Dexela 1512 flat panel detector. A 40kVp x-ray spectrum with a tungsten anode is used for all measurements. The acquisition time for one phase step amounts to 0.1s and the visibility is determined from 128 phase steps over one period of the G2 grating. This large number of phase steps was chosen to reduce the effects of statistical variations due to photon noise and potential inaccuracies in the phase stepping procedure.
The gratings used in the study are fabricated by deep x-ray lithography [26]. The parameters of the gratings G0 and G2 used in the experiment and the inter-grating distances are described in section 3. The design parameters of the two phase gratings G1 used for the experiments is shown in Table 1. One grating has a height of 4.4µm ±0.3µm which corresponds to a π/2-grating for 25keV and the other is a π-shifting-grating with a height of 8.7µm ±0.4µm. In Fig. 2 a photography of one of the gratings is shown. The left side of the grating has a period of 4.37µm and the right side 2.185µm. The three duty cycles are realized in three separated fields in the grating, such that the grating is separated into six tiles on one wafer. For fabrication of the phase gratings, the resist lamellas which are used as template in the electroforming process were patterned as self-standing structures without stabilizing bridges. The resist template has been developed by freeze drying [27]. The duty cycle corresponds to the ratio: (period - width of the resist lamella)/period, whereas the resist height is about 10µm. Not all the duty cycles could be fabricated for two reasons: in case of a large duty cycle, the width of the resist lamella gets rather small resulting in less mechanical stability of lamellas. The lamellae are wavy. In case of a small duty cycle, the distance between two resist lamellas gets very narrow. With decreasing distance the influence of secondary electrons penetrating from the exposed to the unexposed area is increasing [28], leading to crosslinking in the space in between the lamellas and thus hindering a residue free development of the area to be electroformed. This is the case of the combination parameters period 2.185µm and duty cycle 0.33, the space between two resist lamellae being 721nm.
Fig. 2 A photography of one of the used G1 gratings where the six different tiles of grating specifications are visible. From top to bottom, the duty cycle of the grating becomes higher and from left to right, the period changes from 4.37µm to 2.185µm. The correspoding SEM pictures for the two periods and 3 duty cycles presented on the left (4.37µm period; magnification 3000) and on the right (2.185µm period; magnification 4000). The top right field is not presented due to wavy lamellae.
Table 1. Grating specifications of the two G1 gratings used in the experiment.
5. Results and discussion
A fine sampling in terms of the two parameters duty cycle and grating height for the two measured grating periods was obtained by simulation. At the top of Fig. 3 the resulting visibility map for a G1 period of 4.37µm is presented. The G1 period of 2.185µm is shown at the bottom of Fig. 3. These two simulations do not show a congruent result. The effect of changing the duty cycle from the standard-type 0.5 to a higher or lower value increases or decreases the visibility for the 2.185µm period drastically, whereas an increase in the visibility is weaker for the 4.37µm period. This is in accordance with the measurements, see Fig. 4 and Table 2.
Fig. 3 Simulation results: color-coded visibility as a function of the G1 duty cycle and grating height and the two periods 4.37µm (top) and 2.185µm (bottom). The parameters of the measurements are marked with red circles.
Fig. 4 Visibility measured in the second Talbot distance (0.084m) for a π/2-shifting grating with a 40kVp tungsten spectrum. The six tiles seen in the image represent the different G1 specifications seen in table 1. The top row has a duty cycle of 0.33, the middle row of 0.5 and the bottom row of 0.66. The left column has a period of 4.37µm and the right column of 2.185µm. The visibility is color-coded.
Table 2. Measured visibilities for the grating parameters seen in Table 1 and a 40kVp tungsten spectrum.
Furthermore, when varying the grating height simulation and measurement data show the subsequent behavior: For the grating period of 2.185µm and grating heights below 6µm a higher duty cycle delivers a higher visibility. For grating heights above 6µm the inverse effect can be observed. For a grating period of 4.37µm G1 grating structures below 6µm thickness show only a minor improvement if the duty cycle is increased whereas for higher grating structures the best choice lies at a duty cycle of 0.5.
In Fig. 4 the visibility for the π/2-shifting grating (4.4µm ±0.3µm gold thickness) with the three available duty cycles 0.33, 0.5 and 0.66 (from top to bottom) and the two grating periods 4.37µm (left hand side) and 2.185µm (right hand side) is shown, measured in the second Talbot distance and with a 40kVp tungsten-spectrum. The best visibility of 53%±1 % can be reached with a duty cycle of 0.66 and a period of 2.185µm. In comparison to the standard Talbot-Lau type with a duty cycle of 0.5, this corresponds to an increase in visibility of approximately 240 %.
However, the improvement in visibility by increasing the duty cycle of the G1 grating is not generally valid for all Talbot-Lau setups. In Table 2 the measured visibilities for the two investigated G1 gratings is presented. For the π/2-shifting grating with a period of 4.37µm instead of 2.185µm both setups with 0.5 and 0.66 duty cycle show approximately the same value. Further, for the π-shifting grating (8.7µm ±0.4µm Au thickness) the standard setup with 0.5 duty cycles always results in highest visibility. Thus, the best duty cycle is dependent on the period as well as the height of the G1 grating.
The simulated setup parameters for the overall highest visibility (Vmax = 48.22 %) within the evaluated parameter ranges can be found at a grating period of 2.185µm with a bar height of 3.8µm and a duty cycle of 0.68. This expected visibility of 48.22 % is well in accordance with the measured value of Vmeas = 53 %. This agreement indicates that the simulated G1 parameters can be realized with good grating quality.
Furthermore, the achieved improvement in visibility has severe impact on the dose efficiency of the imaging system. According to [17, 18] the noise in a differential phase-contrast acquisition depends on the number of photons N and the visibility V by:
Thus, considering the measured visibilities of 22 % in the standard-type setup and 53 % in the improved version, the potential dose reduction can be calculated. Asking for equal image quality in terms of noise it can be seen that with the proposed grating design the dose can be reduced by a factor of 5.8.
6. Conclusion
In this work we show in simulations and related experiments, that the standard-type Talbot-Lau setup with a duty cycle of 0.5 for the G1 grating is not always the best choice. For some combinations of height and period of the G1 grating an increase in the visibility is achievable if a duty cycle of third-integers is chosen. The angular sensitivity of the system is not changed. Together with the spectrum and the grating periods, the duty cycle of the phase-grating G1 is an important parameter to optimize a setup and to achieve the best visibility for a given set of specifications. This finding has to be considered in optimization procedures. Thereto, the wave field simulation has proven to be an appropriate tool for optimization. The measured visibility of 53%±1 % with a polychromatic source in a laboratory setup leads to an impressive improvement in phase-contrast image quality as the noise in phase-contrast imaging is highly depending on the visibility. Furthermore, this achievement yields the potential to improve dose efficiency and paves the way for x-ray phase-contrast imaging into the clinics.
Acknowledgments
This work was carried out with the support of the Karlsruhe Nano Micro Facility (KNMF), a Helmholtz Research Infrastructure at Karlsruhe Institute of Technology (KIT). We acknowledge support by Deutsche Forschungsgemeinschaftand Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) within the funding programme Open Access Publishing.
References and links
1. A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58, 1–36 (2012). [PubMed]
2. A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 074106 (2007). [CrossRef]
3. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11(19), 2303–2314 (2003). [CrossRef] [PubMed]
4. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005). [CrossRef] [PubMed]
5. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2(4), 258–261 (2006). [CrossRef]
6. T. Koehler, H. Daerr, G. Martens, N. Kuhn, S. Loescher, U. Stevendaal, and E. Roessl, “Slit-scanning differential x-ray phase-contrast mammography: Proof-of-concept experimental studies,” Med. Phys. 42(4), 1959 (2015). [CrossRef] [PubMed]
7. T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical x-ray phase-contrast CT: demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Rad. 45 (7), 445–452 (2010).
8. M. Stampanoni, Z. Wang, T. Thring, C. David, E. Roessl, M. Trippel, R. Kubik-Huch, G. Singer, M. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011). [CrossRef]
9. T. Michel, J. Rieger, G. Anton, F. Bayer, M. Beckmann, J. Durst, P. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58(8), 2713 (2013). [CrossRef] [PubMed]
10. M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast x-ray imaging,” Nat. Sci. Rep. 3, 3209 (2013).
11. K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G.-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41, 011903 (2014). [CrossRef] [PubMed]
12. V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012). [CrossRef]
13. F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21(17), 19922–19933 (2013). [CrossRef] [PubMed]
14. A. Malecki, E. Eggl, F. Schaff, G. Potdevin, T. Baum, E. Garcia, J. Bauer, and F. Pfeiffer, “Correlation of x-ray dark-field radiography to mechanical sample properties,” Microsc. Microanal. 20(5), 1528–1533 (2014). [CrossRef] [PubMed]
15. F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014). [CrossRef]
16. C. Hannesschläger, V. Revol, B. Plank, D. Salaberger, and J. Kastner, “Fibre structure characterisation of injection moulded short fibre-reinforced polymers by X-ray scatter dark field tomography,” Case Studies Nondestructive Testing Eval. 3, 34–41 (2015). [CrossRef]
17. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010). [CrossRef] [PubMed]
18. T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011). [CrossRef] [PubMed]
19. T. Weber, F. Bayer, W. Haas, G. Pelzer, J. Rieger, A. Ritter, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Energy-dependent visibility measurements, their simulation and optimisation of an X-ray Talbot-Lau Interferometer,” JINST 7, P02003 (2012). [CrossRef]
20. A. Hipp, M. Willner, J. Herzen, S. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22(25), 30394–30409 (2014). [CrossRef]
21. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008). [CrossRef]
22. T. Suleski, “Generation of Lohmann images from binary-phase Talbot array illuminators,” Appl. Opt. 36(20), 4686–4691 (1997). [CrossRef] [PubMed]
23. A. Ritter, P. Bartl, F. Bayer, K. Godel, W. Haas, T. Michel, G. Pelzer, J. Rieger, T. Weber, A. Zang, and G. Anton, “Simulation framework for coherent and incoherent X-ray imaging and its application in Talbot-Lau dark-field imaging,” Opt. Express 22(19), 23276–23289 (2014). [CrossRef] [PubMed]
24. K. Morgan, K. Siu, and D. Paganin, “The projection approximation and edge contrast for x-ray propagationbased phase contrast imaging of a cylindrical edge,” Opt. Express 18(10), 9865–9878 (2010). [CrossRef] [PubMed]
25. Siemens.com, “Simulation of X-ray Spectra,” (Siemens.com, 2016), www.siemens.com/x-ray-spectra
26. J. Kenntner, V. Altapova, T. Grund, F. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89 (2012). [CrossRef]
27. F. Koch, F. Marschall, J. Meiser, O. Márkus, A. Faisal, T. Schröter, P. Meyer, D. Kunka, A. Last, and J. Mohr, “Increasing the aperture of x-ray mosaic lenses by freeze drying,” J. Micromech. Microeng. 25(7), 075015 (2015). [CrossRef]
28. P. Meyer and F. Pantenburg, “A Monte Carlo study of the primary absorbed energy redistribution in X-ray lithography,” Microsystem Technologies 20(10), 1881–1889 (2013). [CrossRef]
